I've recently started looking into Genius: the Transgression, but I'm not positive I fully understand the limits of Wonders. Are the things you can make limited by the traits listed under the Axioms, or can you talk with your GM/Storyteller about being able to make things that sound doable with your Axioms/character theme but not explicitly mentioned in the rulebook?

My character is going to have a time/space manipulation theme (eventually), who would hopefully be able to make such things as:

Eye of Chronos: quasi-generic Apokalypsi scanner, at high levels would gain the ability to see forward or backward in time a few minutes.

Spatial Drive: upgrade to said body armor, a rather large back-mounted device that grants the ability to generate wormholes for long-distance travel, or possibly inter-dimensional travel (definitely going to need max Skafoi)

Lightspeed fist: odd combination of Skafoi and Katastrofi, uses time distortion to increase the speed ergo damage of melee attacks (might need ranks of Prostasia to prevent harming oneself, or such a limitation could be left intact for balance purposes).

Those all sound reasonable to this Storyteller. Pg 156 mentions that Apokalypsi includes scanning across time. Using teleportation or time distortion as a mechanism for armor is just a matter of color, and it opens up the possibility of teleporting through a minor obstacle like prison bars - though if you do allow this, you should probably add a comparable weakness, like a chance of splinching if used in a cluttered environment.
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Jon of All TradesFeb 23 '13 at 17:27

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The spatial drive you describe would be a Skafoi device integrated into a Prostasia wonder: no problem per page 140. The lightspeed fist would be a "Grafted" (page 151) Katastrofi weapon with unique color, and as you say self-damage would be a great weakness for it.
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Jon of All TradesFeb 23 '13 at 17:31

Sounds good, though I forgot to mention the lightspeed fist was supposed to be gauntlet-mounted. From what I've seen in the book, that could still work either way. And good point on the teleporter, depending on whether it's instantaneous matter transit or just slowing time around him to give himself relatively instantaneous movement would affect its limitations. I'll have to think about that further.
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CobaltFeb 23 '13 at 18:03

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I think only the system's creator can give a canonical answer. Speaking personally...

In the spirit of roleplaying in general, and of such a wild and open game as Genius, I'd say "hell yeah!" Almost anything a player can describe should be possible, if his or her character has the necessary axioms. Granted, the PDF (I'm referencing the 1.1 version) is ambiguous, suggesting at one point that the axioms are general, and in another that they are indeed limits:

Page 66: Each Axiom covers a general effect or approach [example].

Page 136:
To design a wonder, the genius simply selects one that he can build, based on the limits of his Axioms.

Still, Genius is essentially an evolution of Mage, which definitely does encourage players to come up with their own magic. So even without an explicit rule, I'd absolutely allow creative wonders.

Of course, the axioms are quite broad:

Page 156: The Axiom of Apokalypsi is used to build communicators,
scanners, and analyzers. Anything that transmits information to or
from the genius is the province of this subtle but powerful Axiom.

That covers a lot of ground, and it's just one of eight. Please do give examples, I am quite curious to know what crazy things your group came up with that don't seem to fit any of these!